4 papers
Reduction Complexities in Set Theory
Merlin Carl
In \cite{Ca2016} and \cite{Ca2018}, we introduced a notion of effective reducibility between set-theoretical -statements; in \cite{Ca2025}, this was extended to statements o…
A Note on Power-OTMs
Merlin Carl
We consider the computational strength of Power-OTMs, i.e., ordinal Turing machines equipped with a power set operator, and study a notion of realizability based on these machines.…
Effective Reducibility for Statements of Arbitrary Quantifier Complexity with Ordinal Turing Machines
Merlin Carl
This paper is an extended version of our work in \cite{Ca2025}. We extend the concept of effective reducibility between statements of set theory with ordinal Turing machines (OTMs)…
Recognizable Realizability
Merlin Carl
We introduce a notion of realizability with ordinal Turing machines based on recognizability rather than computability, i.e., the ability to uniquely identify an object. We show th…